Method and apparatus of robust neural temporal coding, learning and cell recruitments for memory using oscillation

ABSTRACT

Certain aspects of the present disclosure support a technique for robust neural temporal coding, learning and cell recruitments for memory using oscillations. Methods are proposed for distinguishing temporal patterns and, in contrast to other “temporal pattern” methods, not merely coincidence of inputs or order of inputs. Moreover, the present disclosure propose practical methods that are biologically-inspired/consistent but reduced in complexity and capable of coding, decoding, recognizing, and learning temporal spike signal patterns. In this disclosure, extensions are proposed to a scalable temporal neural model for robustness, confidence or integrity coding, and recruitment of cells for efficient temporal pattern memory.

BACKGROUND

1. Field

Certain aspects of the present disclosure generally relate to neuralsystem engineering and, more particularly, to a method and apparatus ofrobust neural temporal coding, learning and cell recruitments for memoryusing oscillations.

2. Background

Neurons in a neural system can communicate information temporally usingtemporal codes in the form of timed spikes. Because of this, methods ofcoding and decoding and methods of learning such temporal informationare of primary interest.

In particular, it is desired to distinguish temporal patterns and, incontrast to other temporal pattern methods, not merely coincidence ofinputs or order of inputs. The present disclosure provides methods thatare biologically-inspired/consistent but reduced in complexity andcapable of coding, decoding, recognizing, and learning temporal spikesignal patterns.

SUMMARY

Certain aspects of the present disclosure provide a method of merging anetwork of spiking neuron circuits with a rule for learning synapticweights associated with the neuron circuits. The method generallyincludes providing synaptic inputs into a neuron circuit of the network,wherein each of the synaptic inputs is associated with a synaptic weightof the synaptic weights and a time delay, latching each of the synapticinputs being weighted and delayed, upon a rise in an input of the neuroncircuit comprising the synaptic inputs, and upon the input or upon theneuron circuit spiking based on the rise in the input, applying thelearning rule on the latched synaptic inputs to determine a change inthe synaptic weight associated with that synaptic input.

Certain aspects of the present disclosure provide an electrical circuitfor merging a network of spiking neuron circuits with a rule forlearning synaptic weights associated with the neuron circuits. Theelectrical circuit generally includes a first circuit configured toprovide synaptic inputs into a neuron circuit of the network, whereineach of the synaptic inputs is associated with a synaptic weight and atime delay, a second circuit configured to latch each of the synapticinputs being weighted and delayed, upon a rise in an input of the neuroncircuit comprising the synaptic inputs, and a third circuit configuredto apply, upon the input or upon the neuron circuit spiking based on therise in the input, the learning rule on the latched synaptic inputs todetermine a change in the synaptic weight associated with that synapticinput.

Certain aspects of the present disclosure provide an apparatus formerging a network of spiking neuron circuits with a rule for learningsynaptic weights associated with the neuron circuits. The apparatusgenerally includes means for providing synaptic inputs into a neuroncircuit of the network, wherein each of the synaptic inputs isassociated with a synaptic weight and a time delay, means for latchingeach of the synaptic inputs being weighted and delayed, upon a rise inan input of the neuron circuit comprising the synaptic inputs, and meansfor applying, upon the input or upon the neuron circuit spiking based onthe rise in the input, the learning rule on the latched synaptic inputsto determine a change in the synaptic weight associated with thatsynaptic input.

Certain aspects of the present disclosure provide a method of regulatinga firing rate of a neuron circuit of a neural network. The methodgenerally includes computing periodically the firing rate of the neuroncircuit by counting a number of firings of the neuron circuit within atime period, determining whether the firing rate is below a lower boundor above an upper bound, and adjusting the firing rate by a step amountbased on the determination.

Certain aspects of the present disclosure provide an electrical circuitfor regulating a firing rate of a neuron circuit of a neural network.The electrical circuit generally includes a first circuit configured tocompute periodically the firing rate of the neuron circuit by counting anumber of firings of the neuron circuit within a time period, a secondcircuit configured to determine whether the firing rate is below a lowerbound or above an upper bound, and a third circuit configured to adjustthe firing rate by a step amount based on the determination.

Certain aspects of the present disclosure provide an apparatusregulating a firing rate of a neuron circuit of a neural network. Theapparatus generally includes means for computing periodically the firingrate of the neuron circuit by counting a number of firings of the neuroncircuit within a time period, means for determining whether the firingrate is below a lower bound or above an upper bound, and means foradjusting the firing rate by a step amount based on the determination.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above-recited features of the presentdisclosure can be understood in detail, a more particular description,briefly summarized above, may be had by reference to aspects, some ofwhich are illustrated in the appended drawings. It is to be noted,however, that the appended drawings illustrate only certain typicalaspects of this disclosure and are therefore not to be consideredlimiting of its scope, for the description may admit to other equallyeffective aspects.

FIG. 1 illustrates an example network of neurons in accordance withcertain aspects of the present disclosure.

FIG. 2 illustrates an example relative delay neuron model in accordancewith certain aspects of the present disclosure.

FIG. 3 illustrates an example realignment of relative delay inputs bydendritic model in accordance with certain aspects of the presentdisclosure.

FIG. 4 illustrates an example temporal shift of learning curves inaccordance with certain aspects of the present disclosure.

FIG. 5 illustrates an example temporal shift and sensitivity damping oflearning curves in accordance with certain aspects of the presentdisclosure.

FIG. 6 illustrates example learning curves resulting from dynamicspiking Hebbian rule method in accordance with certain aspects of thepresent disclosure.

FIG. 7 illustrates an example of robustness aspects of the relativedelay neuron model in accordance with certain aspects of the presentdisclosure.

FIG. 8 illustrates an example single oscillation as a basic catalyst forintegrity coding in accordance with certain aspects of the presentdisclosure.

FIG. 9 illustrates an example oscillation reference and integritytemporal coding in accordance with certain aspects of the presentdisclosure.

FIG. 10 illustrates an example oscillation reference and integrity ratecoding in accordance with certain aspects of the present disclosure.

FIG. 11 illustrates an example of connectivity for recruitment of aparticular cell for memory in accordance with certain aspects of thepresent disclosure.

FIG. 12 illustrates an example temporal view of recruitment of aparticular cell for memory in accordance with certain aspects of thepresent disclosure.

FIG. 13 illustrates an example of using oscillation to separate atemporal pattern into highly resolvable sub-patterns in accordance withcertain aspects of the present disclosure.

FIG. 14 illustrates an example of using oscillations to associatepatterns in accordance with certain aspects of the present disclosure.

FIG. 15 illustrates example operations that may be performed at anetwork of neuron circuits in accordance with certain aspects of thepresent disclosure.

FIG. 15A illustrates example components capable of performing theoperations illustrated in FIG. 15.

FIG. 16 illustrates other example operations that may be performed at aneuron circuit of a neural network in accordance with certain aspects ofthe present disclosure.

FIG. 16A illustrates example components capable of performing theoperations illustrated in FIG. 16.

DETAILED DESCRIPTION

Various aspects of the disclosure are described more fully hereinafterwith reference to the accompanying drawings. This disclosure may,however, be embodied in many different forms and should not be construedas limited to any specific structure or function presented throughoutthis disclosure. Rather, these aspects are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of the disclosure to those skilled in the art. Based on theteachings herein one skilled in the art should appreciate that the scopeof the disclosure is intended to cover any aspect of the disclosuredisclosed herein, whether implemented independently of or combined withany other aspect of the disclosure. For example, an apparatus may beimplemented or a method may be practiced using any number of the aspectsset forth herein. In addition, the scope of the disclosure is intendedto cover such an apparatus or method which is practiced using otherstructure, functionality, or structure and functionality in addition toor other than the various aspects of the disclosure set forth herein. Itshould be understood that any aspect of the disclosure disclosed hereinmay be embodied by one or more elements of a claim.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any aspect described herein as “exemplary”is not necessarily to be construed as preferred or advantageous overother aspects.

Although particular aspects are described herein, many variations andpermutations of these aspects fall within the scope of the disclosure.Although some benefits and advantages of the preferred aspects arementioned, the scope of the disclosure is not intended to be limited toparticular benefits, uses or objectives. Rather, aspects of thedisclosure are intended to be broadly applicable to differenttechnologies, system configurations, networks and protocols, some ofwhich are illustrated by way of example in the figures and in thefollowing description of the preferred aspects. The detailed descriptionand drawings are merely illustrative of the disclosure rather thanlimiting, the scope of the disclosure being defined by the appendedclaims and equivalents thereof.

An Example Neural System

FIG. 1 illustrates an example neural system 100 with multiple levels ofneurons in accordance with certain aspects of the present disclosure.The neural system 100 may comprise a level of neurons 102 connected toanother level of neurons 106 though a network of synaptic connections104. For simplicity, only two levels of neurons are illustrated in FIG.1, although fewer or more levels of neurons may exist in a typicalneural system.

As illustrated in FIG. 1, each neuron in the level 102 may receive aninput signal 108 that may be generated by a plurality of neurons of aprevious level (not shown in FIG. 1). The signal 108 may represent aninput current of the level 102 neuron. This current may be accumulatedon the neuron membrane to charge a membrane potential. When the membranepotential reaches its threshold value, the neuron may fire and generatean output spike to be transferred to the next level of neurons (e.g.,the level 106).

The transfer of spikes from one level of neurons to another may beachieved through the network of synaptic connections (or simply“synapses”) 104, as illustrated in FIG. 1. The synapses 104 may receiveoutput signals (i.e., spikes) from the level 102 neurons, scale thosesignals according to adjustable synaptic weights w₁ ^((i,i+1)), . . . ,w_(P) ^((i,i+1)) (where P is a total number of synaptic connectionsbetween the neurons of levels 102 and 106), and combine the scaledsignals as an input signal of each neuron in the level 106. Every neuronin the level 106 may generate output spikes 110 based on thecorresponding combined input signal. The output spikes 110 may be thentransferred to another level of neurons using another network ofsynaptic connections (not shown in FIG. 1).

The neural system 100 may be emulated by an electrical circuit andutilized in a large range of applications, such as image and patternrecognition, machine learning, motor control, and alike. Each neuron inthe neural system 100 may be implemented as a neuron circuit. The neuronmembrane charged to the threshold value initiating the output spike maybe implemented, for example, as a capacitor that integrates anelectrical current flowing through it.

In an aspect, the capacitor may be eliminated as the electrical currentintegrating device of the neuron circuit, and a smaller memristorelement may be used in its place. This approach may be applied in neuroncircuits, as well as in various other applications where bulkycapacitors are utilized as electrical current integrators. In addition,each of the synapses 104 may be implemented based on a memristorelement, wherein synaptic weight changes may relate to changes of thememristor resistance. With nanometer feature-sized memristors, the areaof neuron circuit and synapses may be substantially reduced, which maymake implementation of a very large-scale neural system hardwareimplementation practical.

Since neuron circuits of the neural system 100 may communicateinformation temporally using so-called temporal codes in the form oftimed spikes, the coding and decoding methods as well as methods oflearning such temporal information are of primary interest. Certainaspects of the present disclosure support methods for distinguishingtemporal patterns and, in contrast to other “temporal pattern” methods,not merely coincidence of inputs or order of inputs. Moreover, thepresent disclosure propose practical methods that arebiologically-inspired/consistent but reduced in complexity and capableof coding, decoding, recognizing, and learning temporal spike signalpatterns. In this disclosure, extensions are proposed to a scalabletemporal neural model for robustness, confidence or integrity coding,and recruitment of cells for efficient temporal pattern memory. Theproposed approach is biologically inspired by experimental evidence ofoscillations or rhythms and synchrony, and at the same time, motivatedto reduce modeling complexity.

Relative Delay and Dendritic Delay Lines

A method is proposed in the present disclosure in which a neuron'sbehavior may be determined based on a relative delay between inputs atsynapses, a relative delay between inputs at synapses and a referenceinput, or both. The basic aspect of the temporal coding model isillustrated in FIG. 2. The spatial-temporal pattern of spikes outputfrom neurons 202, 204, 206, 208 (i.e., input neurons) may constitutespike inputs for a neuron 210. Each input neuron may connect to theneuron 210 via one or more synapses on one or more dendrite of theneuron 210. Each synapse may have an associated delay that characterizesthe time delay that a spike from the input neuron undergoes beforereaching the soma of neuron 210, as illustrated in FIG. 2 for synapses212 connecting the neuron 204 with the neuron 210. As illustrated inFIG. 2, the inputs may undergo scaling before delay and integration.Alternatively, the inputs may undergo delay before scaling for reducedprocessing in large-scale networks.

Using this method, a neuron may recognize spatial-temporal patterns inoutputs of input neurons (spatial in the sense of input neurons,temporal in the sense of relative spike timing or temporal differencesbetween spikes). This is illustrated in FIG. 3 where input neurons 302,304, 306, 308 may spike at different times. However, as a result ofdelays in the dendrite(s), signals from the input neurons may reach asoma of output neuron x aligned in time. An input to the output neuron xat time t may thus be expressed as a function of delayed outputs of theinput neurons, i.e.:

$\begin{matrix}{{{u_{x}(t)} = {\sum\limits_{j}{w_{j}{v_{i_{j}}\left( {t - {n_{j}\Delta\; t}} \right)}}}},} & (1)\end{matrix}$where j is the synapse index, i_(j) is the input neuron to which synapsej connects, n_(j) is the synaptic delay in units of Δt, v_(i)(t) is theoutput of input neuron i, and w_(j) is a synaptic weight. In equation(1), the synaptic delay represents a delay by which a total delay isabstracted. That total delay may be due to one or more (combination of)actual synaptic delays due to a digital-to-analog delay (i.e., a timefor conversion from action potential (AP) to post-synaptic potential(PSP)), a dentritic delay (i.e., a passive travel time for the PSP toreach a soma), or other delays (e.g., axonal delays or networkarchitecture delays due to paths through different layers or number ofneurons).

Actual timings of firing of the neurons 302, 304, 306, 308 are labeledas 310 in FIG. 3. Because of particular delays corresponding to synapses(i.e., denoted by multiples of time delay resolution Δt), the inputtimings after delays may or may not align once the relative delays areaccounted for (labeled as 312 in FIG. 3). It can be observed from FIG. 3that some synapses are associated with delays that are too long (e.g., asynapse with delay 314) or short (e.g., a synapse with delay 316) tocoincide with delays of other synapses. In an aspect, these short andlong delays may be discarded from or not added to a recognized pattern,while delays that result in coincident delayed spikes may be retained oradded to correspond to a recognized pattern.

In the preferred aspect of the present disclosure, discrete time delaysof integer milliseconds may be utilized (i.e., delays in multiples oftime delay resolution Δt=1 ms). However, in general, any discrete orcontinuous resolution may be used. In the discrete model, the delay maybe represented by the integer n_(xi), where x is the input neuron (e.g.,the neuron 302 in FIG. 3), and i is the synapse index for that inputneuron since there may be one or more synapses to each input.

In the following, it will be shown how to learn spatial temporalpatterns in a robust manner.

Spike-Based Hebbian Learning Method

A robust reduced method for temporal coding and learning is firstproposed in the present disclosure. Then, this method may be utilized asa basis for a method of further robustness using oscillations andrhythms. In an aspect of the present disclosure, these two methods canbe used together for cell recruitment for memory.

Hebbian learning rules typically operate based on rate-coding or otherwindowed neuron models, adjusting synapse weights based on firing outputover a trial time window. However, spike-based models may be used toreproduce precise timing behavior of neurons, which may fire withparticular delays not necessarily coincident with particular inputsresponsible for causing the firing. Methods used in the reduced modelallow reconciling these differences.

In general, Hebbian learning refers to learning that associates (wirestogether) an input with an output when they occur simultaneously.However, a variety of such rules and related variations can beconsidered relevant for the methods being proposed in the presentdisclosure because of particular temporal aspects. With rate-coding, onemight consider two neurons that are generally firing during a timewindow for association according to Hebbian principles. However, in theproposed methodology, the relative timing of individual spikes may beconsidered. Moreover, because a neuron may fire with some delay afterinputs (causality), “simultaneity” may not be necessarily the optimalassociative condition when considering behavior at the individual spikelevel. This may be important for the reasons discussed below.

Learning synaptic weights can be typically referred to as synapticplasticity. For the Spike-Timing-Dependent Plasticity (STDP), synapticweight adjustments in learning can be typically described in terms of atime difference between when a pre-synaptic input spike occurs and whena post-synaptic neuron fires, referenced by ΔT. Here, the convention canbe used that a positive value means that the pre-synaptic input firedafter the post-synaptic neuron. The learning can be expressed as a curvedescribing the amount and direction of weight adjustment across a rangeof time difference values. It should be noted that a standard STDP curvehas a discontinuity at the origin.

However, an important aspect of learning curves may be shift. Examplesof shifted curves are illustrated in FIG. 4 and FIG. 5. FIG. 4illustrates an example 400 of temporal shift of learning curves inaccordance with certain aspects of the present disclosure. FIG. 5illustrates an example 500 of temporal shift and sensitivity damping oflearning curves in accordance with certain aspects of the presentdisclosure. It should be noted that the shift may be combined with otheraspects, such as reinforcement or de-emphasis variations or other shapeaspects.

Such shifting of the weight learning curve can be motivated for avariety of reasons. First, it may be desired to accommodate neurondepolarization delays (time constant of the soma, for example). In otherwords, if firing is delayed as in biologically motivated dynamic modelsof neurons, it may not be necessary to reinforce synaptic weights forextraneous inputs that may happen to arrive after the sufficientlydepolarizing inputs but before the neuron fires. This may be preventedby shifting the curve toward the left, as illustrated in FIG. 5, whichmay hold the neuron from sliding forward toward the extraneous inputtimes. Second, it may be desired to control (limit) a sliding effectthat may occur if a neuron learns a part of a pattern and startsprecession toward an earlier part of the pattern because of a nominallearning curve shape (i.e., reinforcing synapses with earlier andearlier input arrivals thus causing firing to occur earlier andearlier). This may be prevented by shifting the curve to the rightreinforcing a narrow window of non-causal inputs, which may hold theneuron from sliding backward.

Typical Hebbian plasticity rules applied in the field of theoreticalneuroscience, such as the Oja rule or the BCM rule(Bienenstock-Cooper-Munro rule) and their variations have weightregulation effects, which may stabilize the learning resulting fromthese rules. For example, the Oja's rule may provide weight change (as avector) given by:Δw=v·(u−αvw)·τ,  (2)where v is a neuron's output and u is a neuron's input, τ is a timeconstant controlling weight adaptation (learning) rate and α is aparameter that controls normalization. It can be noticed that at thesteady state u=αvw. Therefore, for coinciding input and output, theweights may be normalized to the value of 1/α. This may have an effectof regulation or so-called homeostasis. It is proposed in the presentdisclosure that neuronal regulation or homeostasis (e.g., maintaining along-term firing rate constant) is an important component. Thus, whenusing STDP or curves such as those illustrated in FIGS. 4-5 (as opposedto the Oja or BCM rules), the addition of neuronal regulation orhomeostasis may be important.

Regarding homeostasis, it may be recommended that rather than targetinga particular firing rate, neurons may be allowed to operate in a firingrate range. Thus, it is proposed in the present disclosure thatthresholds (or inputs) are scaled only if the rate falls beyond an upperor a lower range. This may provide stability as well as flexibility todifferent pattern densities. Thus, it is proposed that such adjustmentis slow, i.e., occurring in the order of at least multiple patternexposures and applied in steps.

However, it can be observed that the STDP-like effects (curves) may bereproduced without actually applying such learning curves directly(i.e., a reduced complexity model). Rather, using such Hebbian rules asthe Oja rule, when combined with a dynamic spiking neuronal model suchas the Izhikevich's simple model, it may be possible to observe thetemporal learning curve effects discussed above (whether similar to theexperimentally observed STDP curves or the variations discussed).

An example of learning curves resulting from dynamic spiking Hebbianrule method is illustrated in FIG. 6. It should be noted that whilethere are similarities with the biologically observed (idealized) STDPcurves, there may exist differences not inconsistent with raw biologicalobserved data where the actual data points are somewhat scattered nearzero. This may also represent motivation to consider such differentcurves as described above. In an aspect, weights may be initially sethigh to encourage excitability and accelerate learning and thedistribution of delay response. Observing a mean curve 602 and a mean ofpositive changes curve 604 illustrated in FIG. 6 may provide insightthat the optimal temporal plasticity curve may not be exactly astypically rendered. It can be observed a relatively flat tail of curve604 as limited negative impact for non-causal (leftward) delays.

However, obtaining these effects without applying the learning curvedirectly may require a critical component, namely that inputs arelatched. The latching may be critical because such learning rules as theOja or BCM rules may typically assume inputs and outputs in terms offiring rate, whereas a dynamic spiking model may spike after some delayfrom the inputs. One way to accomplish this may be to latch inputs whenthe total input increases and maintain the latch until firing. Then, thelatch contents and firing may be utilized according to the learningrule.

Aspects of the above can be seen in the following reduced model oftemporal plasticity. The diagram illustrated in FIG. 6 overlays ascatter plot of weight changes 606 with the mean weight change 602, themean positive weight change 604 and a mean negative weight change 608depending on the delay between firing and the input (at the synapse).The latch operation may be described mathematically as:

$\begin{matrix}{{{{iff}\frac{\mathbb{d}{u(t)}}{\mathbb{d}t}} > 0},{{{then}\mspace{14mu} u_{latch}} = {{u(t)}.}}} & (3)\end{matrix}$

When applying the Oja learning rule (or the BCM or other rule), insteadof using the current values of inputs at the time of firing u(t), thelatched version of inputs u_(latch) may be used. This may have severaladvantages. First, it may not be required to store time stamps andcompute time delays in order to apply the learning curve. Moreover, asmall memory (latch) may be utilized. This may work because the inputmay increase before a neuron fires again (e.g., in the dynamic spikingmodel). Furthermore, variations on this latch condition may be used. Forexample, the largest total input since the last firing may be utilized,wherein it is being referred to the input post dendritic delay.

Learning Stability

Whether applying a Hebbian rule or STDP-like effects, it is proposed inthe present disclosure that weights should be allowed or even designedto polarize (e.g., bipolar tendency to zero or one upon stable learningof a pattern). In other words, it is proposed that a learning ruleshould polarize weights on learning neurons and depolarize weights fornon-learning neurons (neurons reserved for other memories or losing acompetition to code a given pattern).

The reason for this is that the bipolar state (weights tending to zeroor one) resulting from application of learning rules (STDP, Hebbian orotherwise) may have stability advantages when learning multiple patternsor sub-patterns. This may relate to the learning rule nature (e.g.,additive or multiplicative nature). In an aspect, a neuron may beexposed to a pattern that it then learns according to the proposal andthus reaches a bipolar weight state. Subsequent exposure of this neuronwith such bipolar weights (having learned that prior stimulus) to a newstimulus (a different temporal pattern) may provide less chance ofdisturbance of the weights. Thus, it may be less likely for the neuronto unlearn the prior pattern than if the learning rule left the weightsdistributed between zero and one (not bipolar).

Technically, this may occur because for the weights at or near zero,being multiplied by a learning factor to reinforce them counter to theprior pattern, the change may be minimal due to the weight being at ornear zero. In addition, for the weights near one, being multiplied by alearning factor less than one to deemphasize them counter to the priorpattern, the change may be minimal due to the weight being at or nearone. On the other hand, naive synapses, with weights in the middle range(or depolarized), may be much more likely to be recruited for a newpattern. In general, it is thus proposed that whatever method is used toadjust weights, that (a) weights should polarize on competitive winning(learning a given pattern), (b) depolarize otherwise (neurons notallocated to learn the given pattern) and (c) the learning rule shouldbe designed such that polarizing weights may not be easily de-polarized.

Improving Robustness and Confidence

Certain aspects of the present disclosure support a method ofefficiently measuring the confidence or robustness of a pattern matchand a way to translate that into a temporal code. FIG. 7 illustrates anexample 700 for three cases of coincident inputs to a neuron's soma ofvarying magnitudes as a result of synaptic weights, dendritic delays,and combining when exposed to the same pattern.

It should be noted that in order to exceed a firing threshold, thecombined coincident input may generally need to exceed a threshold(relative to resting potential). The contribution of weights, threshold,and number of synapses is depicted in the further description. In a case702 illustrated in FIG. 7, there may be too few coincident synapses (ortoo few weights, or a threshold may 708 be too high). In a case 704, theopposite may occur. Only in a case 706 the match may be perfect. Thecase 704 may be considered being either loose (redundant) or robustdepending on perspective, context or noise level. Similarly, the case706 may be considered perfect (precise or efficient) or sensitive(brittle, non-robust).

It should be also noted that for a given firing, the total contributionof a single input neuron may be determined by the total of synapses withcoincident delay (not merely relative to one another but relative to thecombination with other inputs) and their weights. If the totalcoincident input across input neurons for those synapses is below thethreshold 708, then firing may not occur. On the other hand, if thetotal coincident input across input neurons for those synapses is abovethe threshold 708, then the firing may occur. This may be problematic,as it can be observed from FIG. 7. If, as depicted as the case 704, someparts of the pattern may not be necessary for firing, such as an inputpattern from a neuron 710. Thus, the pattern match confidence may below.

Solution to Robustness

It is proposed in the present disclosure a combination of one or moreaspects to solve these aforementioned problems related to robustness.First, neuronal regulation or homeostasis may be used to control ornormalize total contribution of contributing inputs, in terms of number,weight or otherwise. Thus, a neuron's input level may be adjusted forthe target pattern to correspond to the case 706 from FIG. 7 (i.e.,sufficiently at or above the threshold 708, but not too far over toresult in firing without the correct pattern). In fact, the input levelmay be adjusted by scaling the weights. Also, these weights may beadjusted to give the desired robustness (excess input). This can be abuilding block for the following description of a confidence orintegrity coding method.

It may be desired that an output neuron x matching a temporal spikepattern of input neurons 802, 804, 806, 808 illustrated in FIG. 8. Itcan be noticed that if an oscillation 810 is introduced in a membranepotential or a firing threshold, depending on the phase during which theoutput neuron x considers the inputs may determine how precise the inputmay need to be to match the pattern. In an aspect, the most precisionmay be required at a trough 812 of the oscillation 810. However, at 814or even 816, less precision may be required to fire the neuron. Forexample, at 814, a spike from the neuron 802 may be missing entirely,and, at 816, a spike from the neuron 806 may not be required.

Next, a reference firing may be included, as illustrated in FIG. 9. Anoscillation 902 in combination with a reference neuron firing 904 (e.g.at a trough of the sinusoid 902) may be used to convert confidence intoa temporal code. As illustrated in FIG. 9, the closer the patternrecognizing neuron fires to the reference (trough) 904, the better thematch. Therefore, if an output of the reference neuron 904 and an outputof a matcher neuron 906 are fed into a neuron 908, then a temporallycoded output of the neuron 908 may be used as a confidence measure ofdetecting a spiking pattern 910.

The key aspects of the pattern 910 may be in the spike timing of inputneurons 912, 914, 916, 918. In addition, the reference neuron 904 mayfire on a particular phase based on the oscillation 902. The confidencein the match may be evaluated by the neuron 906, but submitting theoutput of neuron 906 and the reference neuron 904 to the neuron 908 thatcan learn (or be configured) with delays corresponding to the alignment.For example, one possible configuration can be such that if the outputof neuron 906 aligns with the oscillation trough, then the neuron 908may fire, and otherwise it may not. This example shows that in generalany correspondence to oscillation phase may be determined and temporallycoded.

It should be also noted that if the candidate x (or another variant y orz) fires during an up-wave (or down-wave) of the oscillation 902, thenthe pattern 910 may not be exactly matching. In an aspect, by matchingthe temporal difference to the reference time, the neuron 908 may beeasily configured (or learned) to temporally code that poorer quality.It can be noticed that the temporal coding neuron model is utilized asthe basis for all of these neurons.

Essentially, confidence may be a function of oscillation phase, membranetime-constant, and the number and weights of coincident inputs. Hence,oscillation may be used to (a) increase or decrease the sensitivity tothe number of inputs, (b) increase or decrease the sensitivity tocoincidence of inputs, or (c) both.

Probabilistic Confidence and Rate Coding

It should be noted that the confidence may be coded as a rate code byusing a bank of neurons having a range of sensitivities to patternmatching accuracy or confidence. The combined spiking of the neurons mayact as an aggregate spike count or rate code of the confidence (i.e.,more neurons firing means more confidence). For this purpose, outputs ofthe bank of varying-precision neurons may be fed to a rate codingconfidence neuron 1002, as illustrated in FIG. 10. FIG. 10 illustratestwo pattern cases 1004 and 1006, where the first pattern case 1004 mayhave an input matching the pattern so all precision neurons fire and theconfidence may be rate-coded into a high rate spike pattern 1008 fromthe neuron 1002. In the second case, the pattern 1006 may not match aswell, so only a subset of neurons may fire and the neuron 1002 may ratecodes to a slower rate, as illustrated by a spike pattern 1010.

In an aspect of the present disclosure, the neuron 1002 may fire a trainof spikes in a number or rate that is a function of the number ofinputs. This may also be combined with the aforementioned method oftemporal-coding in various combinations (stages or pieces of networkarchitecture) to achieve desired high-level robustness effects.

Recruiting Cells for Memories

It is further proposed in the present disclosure that the aforementionedconcepts of integrity or confidence and precision are particularlyrelevant for memory aspects. FIG. 11 illustrates a network 1102 of alarge number of interconnected neurons, which may be exposed to aparticular input that is desired to be remembered by the network 1102.An important question to answer is whether it is necessary for thenetwork 1102 to remember (code) the output of every single neuron inorder for it to be able to recognize this input the next time thenetwork is exposed to this particular input pattern. Another importantquestion to answer is whether it is necessary for the network toremember (code) the output of all of its highest-layer (output) neurons.

It is suggested in the present disclosure that such a global or largescale memory is not only unnecessary but also inefficient. Instead, amethod is proposed by which a few (even one) neuron's output may besufficient to remember the input pattern. It is also disclosed how sucha cell or cells recruited by a network system and a memory can belearned.

A method is proposed in the present disclosure to identify a key neuronor neurons for a memory by using, in part, the above proposed confidencemethod. It is shown how applying an oscillation can identify whichneurons are particularly tuned to exact pattern(s) by either thetemporal confidence code or probabilistic/rate code. Thus, it may bepossible to identify and recruit this cell or cells for a particularmemory. This particular cell or cells may be then connected (weightsreinforced) to the memory cell inputs to be learned. With a memory cellbank and lateral inhibition, highly efficient storage of many patternsmay thus be achieved.

This can be explained in the context of FIG. 11 where the network layeror layers 1102 are abstracted. Inputs 1104 may be fed to the network1102, and neurons 1106, 1108, 1110 may represent few neurons in thenetwork 1102. It may be possible to determine which is the most precisetemporal coding match for a given input, and assign that as a dominant(or only) input for a memory cell (e.g., the neuron 1106). In a sense,the neuron 1106 can be called the “memory neuron”, but the m cell 1112is referred to as the memory cell because it may code the coincidence ofoscillation reference 1114 and the output of neuron 1106.

This selection process may be also performed with the Hebbian learningrule. Accordingly, coincident input and output may be wired together sothat a memory neuron learns the coincidence. In this case, many networkneurons may be initially connected to one or more memory cells, and thenthe correspondence with the reference may be learned by adaptingweights. For example, in FIG. 11, a weight of synapse connecting theneuron 1106 and the cell 1112 may represent a strong weight. It shouldbe noted that a temporal pattern model may not be required for thememory neuron because the temporal coding may occur in the networklayers. This can be explained in the context of FIG. 12.

In FIG. 12, it is apparent that a neuron 1202 most precisely codes theinput pattern because it fires with the least offset from theoscillation trough. If a memory cell with minimal temporal coding delayrange (i.e. mainly a coincidence coder) is used (i.e., a memory cell1204), then the memory cell 1204 may be trained to fire for the mostcoincident input, which would be inputs 1202 and 1206. Thus, a mechanismmay be developed in the present disclosure for remembering an inputpattern with minimal resources (neurons).

Robustness over Long Time Frames

Furthermore, it is proposed in the present disclosure that by feeding aninput to different parts of a network subject to different oscillationfrequencies or offsets (example shown in FIG. 13), these parts of atemporal pattern of input may be separated (isolated) for robust patternmatching within those network parts and then the results may berecombined. In a highly efficient network, this may even occur bypassing the pattern matching back and forth between two network parts asthe oscillation peaks in one or the other.

A network may also be configured with only one oscillation and merelysample parts of a pattern but thereby separate the pattern into clearlyseparated parts in order to “clear” individual neuron states betweensections and improve coding/recognition fidelity.

Temporally Correlated Memories

In an aspect, two temporally coded symbolic memories can be considered,which are desired to be connected (associated) to each other. In anaspect, oscillation (rhythms) may be used to re-align neuronalassemblies to obtain any desired overlap that can be encoded temporally.To understand how to do this, the temporal-confidence coding buildingblock described above can be considered.

FIG. 14 illustrates a spatial-temporal input pattern 1402 withrectangles indicating portions of the pattern recognized by particularneurons (in the absence of oscillation, i.e., high fidelity). Now, twooscillations 1404-1406 may be added, each rhythm applied to twocircuits—one circuit comprising neurons 1408 and another circuitcomprising neurons 1410. If these two sets of neurons are considered tobe two temporal confidence codes, these neurons may be brought intoalignment for a secondary coincidence coding by (phase) shifting orscaling (changing the frequency) of the oscillation. It should be notedthat with oscillation up-phases, the neurons may fire earlier because ofthe less stringent conditions. By bringing the two into a resolvabletime window, then their association may be coded.

FIG. 15 illustrates example operations 1500 that may be performed at anetwork of spiking neuron circuits for merging the network with a rulefor learning synaptic weights associated with the neuron circuits inaccordance with certain aspects of the present disclosure. At 1502,synaptic inputs may be provided into a neuron circuit of the network,wherein each of the synaptic inputs may be associated with a synapticweight and a time delay. At 1504, each of the synaptic inputs beingweighted and delayed may be latched upon a rise in an input of theneuron circuit comprising the synaptic inputs. At 1506, upon the inputor upon the neuron circuit spiking based on the rise in the input, thelearning rule may be applied on the latched synaptic inputs to determinea change in the synaptic weight associated with that synaptic input.

In an aspect, that weighed and delayed synaptic inputs may be latchedwhen the input of neuron circuit is at a largest value since the neuroncircuit fired last time. According to certain aspects of the presentdisclosure, the learning rule may correspond to one of real-valuedHebbian learning rules, such as the Oja learning rule. Further, theapplied learning rule may polarize the synaptic weight associated withthat synaptic input. Also, the learning rule may be associated with ashifted STDP learning curve to compensate for a delay from a definedlevel of depolarization of the synaptic inputs to spiking of the neuroncircuit.

In an aspect, the time delay may be equal to one or more multiples of atime delay resolution. The input of neuron circuit may comprise a sum ofthe synaptic inputs, wherein each of the summed synaptic inputs may beassociated with a synapse characterized by the weight and the time delay(e.g., as defined by equation (1)).

In one aspect, the neuron circuit and the synaptic inputs may beassociated with a dynamic spiking neuron model. In another aspect, theneuron circuit and the synaptic inputs may be associated with aleaky-integrate-and-fire neuron model.

In an aspect of the present disclosure, as illustrated in FIG. 9, adifference in time between firing of the neuron circuit and firing of areference neuron circuit of the network may be utilized to temporallycode an output of another neuron circuit of the network. The temporallycoded output may comprise information about a confidence that a spikingpattern of the synaptic inputs matches a defined pattern, while outputsof the neuron circuit and the reference neuron circuit may be fed intothe other neuron circuit to generate the temporally coded output. Inanother aspect, as illustrated in FIG. 10, an output of the neuroncircuit may be provided into another neuron circuit of the network togenerate an output of the other neuron circuit. Then, a firing rate ofthe output of other neuron circuit may indicate a confidence that aspiking pattern of the synaptic inputs into the neuron circuit matches adefined pattern.

In one aspect of the present disclosure, as illustrated in FIGS. 11-12,one of the neuron circuits may be selected as a memory cell to memorizea spiking pattern fed into the network, while oscillation may be appliedat an input of a reference neuron circuit of the network. The selectionmay be based on that neuron circuit responding to the spiking patternclosest to a trough of the oscillation among a set of the neuroncircuits.

FIG. 16 illustrates example operations 1600 that may be performed at aneuron circuit of a neural network in accordance with certain aspects ofthe present disclosure. At 1602, a firing rate of the neuron circuit maybe computed periodically by counting a number of firings of the neuroncircuit within a time period. At 1604, it may be determined whether thefiring rate is below a lower bound or above an upper bound. At 1606, thefiring rate may be adjusted by a step amount based on the determination.

In an aspect of the present disclosure, adjusting the firing rate maycomprise boosting the firing rate, if the computed firing rate is belowthe lower bound. In another aspect, adjusting the firing rate maycomprise dampening the firing rate, if the computed firing rate is abovethe upper bound.

According to certain aspects of the present disclosure, a commonmultiplier may be applied to all synaptic inputs of the neuron circuitto regulate the firing rate. In an aspect, adjusting the firing rate bythe step amount may be achieved by adjusting the applied multiplier.

The various operations of methods described above may be performed byany suitable means capable of performing the corresponding functions.The means may include various hardware and/or software component(s)and/or module(s), including, but not limited to a circuit, anapplication specific integrate circuit (ASIC), or processor. Generally,where there are operations illustrated in Figures, those operations mayhave corresponding counterpart means-plus-function components withsimilar numbering. For example, operations 1500 and 1600 illustrated inFIG. 15 and FIG. 16 correspond to components 1500A and 1600A illustratedin FIG. 15A and FIG. 16A.

As used herein, the term “determining” encompasses a wide variety ofactions. For example, “determining” may include calculating, computing,processing, deriving, investigating, looking up (e.g., looking up in atable, a database or another data structure), ascertaining and the like.Also, “determining” may include receiving (e.g., receiving information),accessing (e.g., accessing data in a memory) and the like. Also,“determining” may include resolving, selecting, choosing, establishingand the like.

As used herein, a phrase referring to “at least one of” a list of itemsrefers to any combination of those items, including single members. Asan example, “at least one of: a, b, or c” is intended to cover: a, b, c,a-b, a-c, b-c, and a-b-c.

The various operations of methods described above may be performed byany suitable means capable of performing the operations, such as varioushardware and/or software component(s), circuits, and/or module(s).Generally, any operations illustrated in the Figures may be performed bycorresponding functional means capable of performing the operations.

The various illustrative logical blocks, modules and circuits describedin connection with the present disclosure may be implemented orperformed with a general purpose processor, a digital signal processor(DSP), an application specific integrated circuit (ASIC), a fieldprogrammable gate array signal (FPGA) or other programmable logic device(PLD), discrete gate or transistor logic, discrete hardware componentsor any combination thereof designed to perform the functions describedherein. A general purpose processor may be a microprocessor, but in thealternative, the processor may be any commercially available processor,controller, microcontroller or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration.

The steps of a method or algorithm described in connection with thepresent disclosure may be embodied directly in hardware, in a softwaremodule executed by a processor, or in a combination of the two. Asoftware module may reside in any form of storage medium that is knownin the art. Some examples of storage media that may be used includerandom access memory (RAM), read only memory (ROM), flash memory, EPROMmemory, EEPROM memory, registers, a hard disk, a removable disk, aCD-ROM and so forth. A software module may comprise a singleinstruction, or many instructions, and may be distributed over severaldifferent code segments, among different programs, and across multiplestorage media. A storage medium may be coupled to a processor such thatthe processor can read information from, and write information to, thestorage medium. In the alternative, the storage medium may be integralto the processor.

The methods disclosed herein comprise one or more steps or actions forachieving the described method. The method steps and/or actions may beinterchanged with one another without departing from the scope of theclaims. In other words, unless a specific order of steps or actions isspecified, the order and/or use of specific steps and/or actions may bemodified without departing from the scope of the claims.

The functions described may be implemented in hardware, software,firmware, or any combination thereof. If implemented in software, thefunctions may be stored or transmitted over as one or more instructionsor code on a computer-readable medium. Computer-readable media includeboth computer storage media and communication media including any mediumthat facilitates transfer of a computer program from one place toanother. A storage medium may be any available medium that can beaccessed by a computer. By way of example, and not limitation, suchcomputer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or otheroptical disk storage, magnetic disk storage or other magnetic storagedevices, or any other medium that can be used to carry or store desiredprogram code in the form of instructions or data structures and that canbe accessed by a computer. Also, any connection is properly termed acomputer-readable medium. For example, if the software is transmittedfrom a website, server, or other remote source using a coaxial cable,fiber optic cable, twisted pair, digital subscriber line (DSL), orwireless technologies such as infrared (IR), radio, and microwave, thenthe coaxial cable, fiber optic cable, twisted pair, DSL, or wirelesstechnologies such as infrared, radio, and microwave are included in thedefinition of medium. Disk and disc, as used herein, include compactdisc (CD), laser disc, optical disc, digital versatile disc (DVD),floppy disk, and Blu-ray® disc where disks usually reproduce datamagnetically, while discs reproduce data optically with lasers. Thus, insome aspects computer-readable media may comprise non-transitorycomputer-readable media (e.g., tangible media). In addition, for otheraspects computer-readable media may comprise transitorycomputer-readable media (e.g., a signal). Combinations of the aboveshould also be included within the scope of computer-readable media.

Thus, certain aspects may comprise a computer program product forperforming the operations presented herein. For example, such a computerprogram product may comprise a computer readable medium havinginstructions stored (and/or encoded) thereon, the instructions beingexecutable by one or more processors to perform the operations describedherein. For certain aspects, the computer program product may includepackaging material.

Software or instructions may also be transmitted over a transmissionmedium. For example, if the software is transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition oftransmission medium.

Further, it should be appreciated that modules and/or other appropriatemeans for performing the methods and techniques described herein can bedownloaded and/or otherwise obtained by a user terminal and/or basestation as applicable. For example, such a device can be coupled to aserver to facilitate the transfer of means for performing the methodsdescribed herein. Alternatively, various methods described herein can beprovided via storage means (e.g., RAM, ROM, a physical storage mediumsuch as a compact disc (CD) or floppy disk, etc.), such that a userterminal and/or base station can obtain the various methods uponcoupling or providing the storage means to the device. Moreover, anyother suitable technique for providing the methods and techniquesdescribed herein to a device can be utilized.

It is to be understood that the claims are not limited to the preciseconfiguration and components illustrated above. Various modifications,changes and variations may be made in the arrangement, operation anddetails of the methods and apparatus described above without departingfrom the scope of the claims.

While the foregoing is directed to aspects of the present disclosure,other and further aspects of the disclosure may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

The invention claimed is:
 1. A method of merging a network of spikingneuron circuits with a rule for learning synaptic weights associatedwith the neuron circuits, comprising: providing synaptic inputs into aneuron circuit of the network, wherein each of the synaptic inputs isassociated with a synaptic weight and a time delay; latching each of thesynaptic inputs being weighted and delayed, upon a rise in an input ofthe neuron circuit comprising the synaptic inputs; and upon the input orupon the neuron circuit spiking based on the rise in the input, applyingthe learning rule on the latched synaptic inputs to determine a changein the synaptic weight associated with that synaptic input.
 2. Themethod of claim 1, wherein the learning rule comprises a real-valuedHebbian learning rule.
 3. The method of claim 2, wherein the Hebbianlearning rule comprises the Oja learning rule.
 4. The method of claim 1,wherein the time delay is equal to one or more multiples of a time delayresolution.
 5. The method of claim 1, wherein the input of neuroncircuit comprises a sum of the synaptic inputs, wherein each of thesummed synaptic inputs is associated with a synapse characterized by thesynaptic weight and the time delay.
 6. The method of claim 1, whereinlatching comprises: latching the weighed and delayed synaptic inputswhen the input of neuron circuit is at a largest value since the neuroncircuit fired last time.
 7. The method of claim 1, wherein latchingcomprises: latching the weighed and delayed synaptic inputs upon anyincrease in the input of neuron circuit.
 8. The method of claim 1,wherein the applied learning rule polarizes the synaptic weightassociated with that synaptic input.
 9. The method of claim 1, whereinthe neuron circuit and the synaptic inputs are associated with a dynamicspiking neuron model.
 10. The method of claim 1, wherein the neuroncircuit and the synaptic inputs are associated with aleaky-integrate-and-fire neuron model.
 11. The method of claim 1,wherein the learning rule is associated with a shiftedSpike-Timing-Dependent Plasticity (STDP) learning curve to compensatefor a delay from a defined level of depolarization of the synapticinputs to spiking of the neuron circuit.
 12. The method of claim 1,further comprising: utilizing a difference in time between firing of theneuron circuit and firing of a reference neuron circuit of the networkto temporally code an output of another neuron circuit of the network,wherein the temporally coded output comprises information about aconfidence that a spiking pattern of the synaptic inputs matches adefined pattern, and outputs of the neuron circuit and the referenceneuron circuit are fed into the other neuron circuit to generate thetemporally coded output.
 13. The method of claim 1, further comprising:providing an output of the neuron circuit into another neuron circuit ofthe network to generate an output of the other neuron circuit, wherein afiring rate of the output of other neuron circuit indicates a confidencethat a spiking pattern of the synaptic inputs into the neuron circuitmatches a defined pattern.
 14. The method of claim 1, furthercomprising: selecting, using oscillation at an input of a referenceneuron circuit of the network, one of the neuron circuits as a memorycell to memorize a spiking pattern fed into the network, wherein theselection is based on that neuron circuit responding to the spikingpattern closest to a trough of the oscillation among a set of the neuroncircuits.
 15. An electrical circuit for merging a network of spikingneuron circuits with a rule for learning synaptic weights associatedwith the neuron circuits, comprising: a first circuit configured toprovide synaptic inputs into a neuron circuit of the network, whereineach of the synaptic inputs is associated with a synaptic weight and atime delay; a second circuit configured to latch each of the synapticinputs being weighted and delayed, upon a rise in an input of the neuroncircuit comprising the synaptic inputs; and a third circuit configuredto apply, upon the input or upon the neuron circuit spiking based on therise in the input, the learning rule on the latched synaptic inputs todetermine a change in the synaptic weight associated with that synapticinput.
 16. The electrical circuit of claim 15, wherein the learning rulecomprises a real-valued Hebbian learning rule.
 17. The electricalcircuit of claim 16, wherein the Hebbian learning rule comprises the Ojalearning rule.
 18. The electrical circuit of claim 15, wherein the timedelay is equal to one or more multiples of a time delay resolution. 19.The electrical circuit of claim 15, wherein the input of neuron circuitcomprises a sum of the synaptic inputs, wherein each of the summedsynaptic inputs is associated with a synapse characterized by thesynaptic weight and the time delay.
 20. The electrical circuit of claim15, wherein the second circuit is also configured to latch the weighedand delayed synaptic inputs when the input of neuron circuit is at alargest value since the neuron circuit fired last time.
 21. Theelectrical circuit of claim 15, wherein the second circuit is alsoconfigured to latch the weighed and delayed synaptic inputs upon anyincrease in the input of neuron circuit.
 22. The electrical circuit ofclaim 15, wherein the applied learning rule polarizes the synapticweight associated with that synaptic input.
 23. The electrical circuitof claim 15, wherein the neuron circuit and the synaptic inputs areassociated with a dynamic spiking neuron model.
 24. The electricalcircuit of claim 15, wherein the neuron circuit and the synaptic inputsare associated with a leaky-integrate-and-fire neuron model.
 25. Theelectrical circuit of claim 15, wherein the learning rule is associatedwith a shifted Spike-Timing-Dependent Plasticity (STDP) learning curveto compensate for a delay from a defined level of depolarization of thesynaptic inputs to spiking of the neuron circuit.
 26. The electricalcircuit of claim 15, further comprising: a fourth circuit configured toutilize a difference in time between firing of the neuron circuit andfiring of a reference neuron circuit of the network to temporally codean output of another neuron circuit of the network, wherein thetemporally coded output comprises information about a confidence that aspiking pattern of the synaptic inputs matches a defined pattern, andoutputs of the neuron circuit and the reference neuron circuit are fedinto the other neuron circuit to generate the temporally coded output.27. The electrical circuit of claim 15, further comprising: a fourthcircuit configured to provide an output of the neuron circuit intoanother neuron circuit of the network to generate an output of the otherneuron circuit, wherein a firing rate of the output of other neuroncircuit indicates a confidence that a spiking pattern of the synapticinputs into the neuron circuit matches a defined pattern.
 28. Theelectrical circuit of claim 15, further comprising: a fourth circuitconfigured to select, using oscillation at an input of a referenceneuron circuit of the network, one of the neuron circuits as a memorycell to memorize a spiking pattern fed into the network, wherein theselection is based on that neuron circuit responding to the spikingpattern closest to a trough of the oscillation among a set of the neuroncircuits.
 29. An apparatus for merging a network of spiking neuroncircuits with a rule for learning synaptic weights associated with theneuron circuits, comprising: means for providing synaptic inputs into aneuron circuit of the network, wherein each of the synaptic inputs isassociated with a synaptic weight and a time delay; means for latchingeach of the synaptic inputs being weighted and delayed, upon a rise inan input of the neuron circuit comprising the synaptic inputs; and meansfor applying, upon the input or upon the neuron circuit spiking based onthe rise in the input, the learning rule on the latched synaptic inputsto determine a change in the synaptic weight associated with thatsynaptic input.
 30. The apparatus of claim 29, wherein the learning rulecomprises a real-valued Hebbian learning rule.
 31. The apparatus ofclaim 30, wherein the Hebbian learning rule comprises the Oja learningrule.
 32. The apparatus of claim 29, wherein the time delay is equal toone or more multiples of a time delay resolution.
 33. The apparatus ofclaim 29, wherein the input of neuron circuit comprises a sum of thesynaptic inputs, wherein each of the summed synaptic inputs isassociated with a synapse characterized by the synaptic weight and thetime delay.
 34. The apparatus of claim 29, further comprising: means forlatching the weighed and delayed synaptic inputs when the input ofneuron circuit is at a largest value since the neuron circuit fired lasttime.
 35. The apparatus of claim 29, further comprising: means forlatching the weighed and delayed synaptic inputs upon any increase inthe input of neuron circuit.
 36. The apparatus of claim 29, wherein theapplied learning rule polarizes the synaptic weight associated with thatsynaptic input.
 37. The apparatus of claim 29, wherein the neuroncircuit and the synaptic inputs are associated with a dynamic spikingneuron model.
 38. The apparatus of claim 29, wherein the neuron circuitand the synaptic inputs are associated with a leaky-integrate-and-fireneuron model.
 39. The apparatus of claim 29, wherein the learning ruleis associated with a shifted Spike-Timing-Dependent Plasticity (STDP)learning curve to compensate for a delay from a defined level ofdepolarization of the synaptic inputs to spiking of the neuron circuit.40. The apparatus of claim 29, further comprising: means for utilizing adifference in time between firing of the neuron circuit and firing of areference neuron circuit of the network to temporally code an output ofanother neuron circuit of the network, wherein the temporally codedoutput comprises information about a confidence that a spiking patternof the synaptic inputs matches a defined pattern, and outputs of theneuron circuit and the reference neuron circuit are fed into the otherneuron circuit to generate the temporally coded output.
 41. Theapparatus of claim 29, further comprising: means for providing an outputof the neuron circuit into another neuron circuit of the network togenerate an output of the other neuron circuit, wherein a firing rate ofthe output of other neuron circuit indicates a confidence that a spikingpattern of the synaptic inputs into the neuron circuit matches a definedpattern.
 42. The apparatus of claim 29, further comprising: means forselecting, using oscillation at an input of a reference neuron circuitof the network, one of the neuron circuits as a memory cell to memorizea spiking pattern fed into the network, wherein the selection is basedon that neuron circuit responding to the spiking pattern closest to atrough of the oscillation among a set of the neuron circuits.
 43. Acomputer program product for merging a network of spiking neuroncircuits with a rule for learning synaptic weights associated with theneuron circuits, comprising a non-transitory computer-readable mediumcomprising code for: providing synaptic inputs into a neuron circuit ofthe network, wherein each of the synaptic inputs is associated with asynaptic weight and a time delay; latching each of the synaptic inputsbeing weighted and delayed, upon a rise in an input of the neuroncircuit comprising the synaptic inputs; and upon the input or upon theneuron circuit spiking based on the rise in the input, applying thelearning rule on the latched synaptic inputs to determine a change inthe synaptic weight associated with that synaptic input.
 44. Thecomputer program product of claim 43, wherein the learning rulecomprises a real-valued Hebbian learning rule.
 45. The computer programproduct of claim 44, wherein the Hebbian learning rule comprises the Ojalearning rule.
 46. The computer program product of claim 43, wherein thetime delay is equal to one or more multiples of a time delay resolution.47. The computer program product of claim 43, wherein the input ofneuron circuit comprises a sum of the synaptic inputs, wherein each ofthe summed synaptic inputs is associated with a synapse characterized bythe synaptic weight and the time delay.
 48. The computer program productof claim 43, wherein the computer-readable medium further comprises codefor: latching the weighed and delayed synaptic inputs when the input ofneuron circuit is at a largest value since the neuron circuit fired lasttime.
 49. The computer program product of claim 43, wherein thecomputer-readable medium further comprises code for: latching theweighed and delayed synaptic inputs upon any increase in the input ofneuron circuit.
 50. The computer program product of claim 43, whereinthe applied learning rule polarizes the synaptic weight associated withthat synaptic input.
 51. The computer program product of claim 43,wherein the neuron circuit and the synaptic inputs are associated with adynamic spiking neuron model.
 52. The computer program product of claim43, wherein the neuron circuit and the synaptic inputs are associatedwith a leaky-integrate-and-fire neuron model.
 53. The computer programproduct of claim 43, wherein the learning rule is associated with ashifted Spike-Timing-Dependent Plasticity (STDP) learning curve tocompensate for a delay from a defined level of depolarization of thesynaptic inputs to spiking of the neuron circuit.
 54. The computerprogram product of claim 43, wherein the computer-readable mediumfurther comprises code for: utilizing a difference in time betweenfiring of the neuron circuit and firing of a reference neuron circuit ofthe network to temporally code an output of another neuron circuit ofthe network, wherein the temporally coded output comprises informationabout a confidence that a spiking pattern of the synaptic inputs matchesa defined pattern, and outputs of the neuron circuit and the referenceneuron circuit are fed into the other neuron circuit to generate thetemporally coded output.
 55. The computer program product of claim 43,wherein the computer-readable medium further comprises code for:providing an output of the neuron circuit into another neuron circuit ofthe network to generate an output of the other neuron circuit, wherein afiring rate of the output of other neuron circuit indicates a confidencethat a spiking pattern of the synaptic inputs into the neuron circuitmatches a defined pattern.
 56. The computer program product of claim 43,wherein the computer-readable medium further comprises code for:selecting, using oscillation at an input of a reference neuron circuitof the network, one of the neuron circuits as a memory cell to memorizea spiking pattern fed into the network, wherein the selection is basedon that neuron circuit responding to the spiking pattern closest to atrough of the oscillation among a set of the neuron circuits.